LMFDB - Embedded newform 1776.2.q.h.433.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1776,2,Mod(433,1776)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1776.433"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1776, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1776 = 2^{4} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1776.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-2,0,-1,0,3,0,-2,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.1814313990$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 222)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			433.1
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	1776.433
Dual form			1776.2.q.h.1009.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{3} +(-1.68614 + 2.92048i) q^{5} +(2.18614 - 3.78651i) q^{7} +(-0.500000 - 0.866025i) q^{9} -2.00000 q^{11} +(2.18614 - 3.78651i) q^{13} +(-1.68614 - 2.92048i) q^{15} +(3.68614 + 6.38458i) q^{17} +(-3.37228 + 5.84096i) q^{19} +(2.18614 + 3.78651i) q^{21} +(-3.18614 - 5.51856i) q^{25} +1.00000 q^{27} -1.37228 q^{29} +3.62772 q^{31} +(1.00000 - 1.73205i) q^{33} +(7.37228 + 12.7692i) q^{35} +(6.05842 + 0.543620i) q^{37} +(2.18614 + 3.78651i) q^{39} +(-0.686141 + 1.18843i) q^{41} +3.62772 q^{43} +3.37228 q^{45} -2.00000 q^{47} +(-6.05842 - 10.4935i) q^{49} -7.37228 q^{51} +(5.74456 + 9.94987i) q^{53} +(3.37228 - 5.84096i) q^{55} +(-3.37228 - 5.84096i) q^{57} +(-2.00000 - 3.46410i) q^{59} +(-4.05842 + 7.02939i) q^{61} -4.37228 q^{63} +(7.37228 + 12.7692i) q^{65} +(-6.55842 + 11.3595i) q^{67} +(-5.74456 + 9.94987i) q^{71} +8.37228 q^{73} +6.37228 q^{75} +(-4.37228 + 7.57301i) q^{77} +(-2.18614 + 3.78651i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(4.00000 + 6.92820i) q^{83} -24.8614 q^{85} +(0.686141 - 1.18843i) q^{87} +(-4.68614 - 8.11663i) q^{89} +(-9.55842 - 16.5557i) q^{91} +(-1.81386 + 3.14170i) q^{93} +(-11.3723 - 19.6974i) q^{95} -5.74456 q^{97} +(1.00000 + 1.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - q^{5} + 3 q^{7} - 2 q^{9} - 8 q^{11} + 3 q^{13} - q^{15} + 9 q^{17} - 2 q^{19} + 3 q^{21} - 7 q^{25} + 4 q^{27} + 6 q^{29} + 26 q^{31} + 4 q^{33} + 18 q^{35} + 7 q^{37} + 3 q^{39} + 3 q^{41}+ \cdots + 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - q^5 + 3 * q^7 - 2 * q^9 - 8 * q^11 + 3 * q^13 - q^15 + 9 * q^17 - 2 * q^19 + 3 * q^21 - 7 * q^25 + 4 * q^27 + 6 * q^29 + 26 * q^31 + 4 * q^33 + 18 * q^35 + 7 * q^37 + 3 * q^39 + 3 * q^41 + 26 * q^43 + 2 * q^45 - 8 * q^47 - 7 * q^49 - 18 * q^51 + 2 * q^55 - 2 * q^57 - 8 * q^59 + q^61 - 6 * q^63 + 18 * q^65 - 9 * q^67 + 22 * q^73 + 14 * q^75 - 6 * q^77 - 3 * q^79 - 2 * q^81 + 16 * q^83 - 42 * q^85 - 3 * q^87 - 13 * q^89 - 21 * q^91 - 13 * q^93 - 34 * q^95 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1776\mathbb{Z}\right)^\times$.

$n$	$223$	$593$	$1297$	$1333$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$	−1.68614	+	2.92048i	−0.754065	+	1.30608i	0.191773	+	0.981439i	$0.438576\pi$
$5$	−1.68614	+	2.92048i	−0.754065	+	1.30608i	−0.945838	+	0.324640i	$0.894757\pi$
$6$		0			0
$7$	2.18614	−	3.78651i	0.826284	−	1.43117i	−0.0746509	−	0.997210i	$-0.523784\pi$
$7$	2.18614	−	3.78651i	0.826284	−	1.43117i	0.900934	−	0.433955i	$-0.142882\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		0			0
$13$	2.18614	−	3.78651i	0.606326	−	1.05019i	−0.385514	−	0.922702i	$-0.625976\pi$
$13$	2.18614	−	3.78651i	0.606326	−	1.05019i	0.991840	−	0.127486i	$-0.0406908\pi$
$14$		0			0
$15$	−1.68614	−	2.92048i	−0.435360	−	0.754065i
$16$		0			0
$17$	3.68614	+	6.38458i	0.894020	+	1.54849i	0.835012	+	0.550231i	$0.185460\pi$
$17$	3.68614	+	6.38458i	0.894020	+	1.54849i	0.0590081	+	0.998258i	$0.481206\pi$
$18$		0			0
$19$	−3.37228	+	5.84096i	−0.773654	+	1.34001i	0.161893	+	0.986808i	$0.448240\pi$
$19$	−3.37228	+	5.84096i	−0.773654	+	1.34001i	−0.935548	+	0.353200i	$0.885093\pi$
$20$		0			0
$21$	2.18614	+	3.78651i	0.477055	+	0.826284i
$22$		0			0
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$		0			0
$25$	−3.18614	−	5.51856i	−0.637228	−	1.10371i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−1.37228			−0.254826			−0.127413	−	0.991850i	$-0.540667\pi$
$29$	−1.37228			−0.254826			−0.127413	+	0.991850i	$0.540667\pi$
$30$		0			0
$31$	3.62772			0.651558			0.325779	−	0.945446i	$-0.394374\pi$
$31$	3.62772			0.651558			0.325779	+	0.945446i	$0.394374\pi$
$32$		0			0
$33$	1.00000	−	1.73205i	0.174078	−	0.301511i
$34$		0			0
$35$	7.37228	+	12.7692i	1.24614	+	2.15838i
$36$		0			0
$37$	6.05842	+	0.543620i	0.995998	+	0.0893706i
$37$	6.05842	+	0.543620i	0.995998	+	0.0893706i
$38$		0			0
$39$	2.18614	+	3.78651i	0.350063	+	0.606326i
$40$		0			0
$41$	−0.686141	+	1.18843i	−0.107157	+	0.185602i	−0.914617	−	0.404320i	$-0.867508\pi$
$41$	−0.686141	+	1.18843i	−0.107157	+	0.185602i	0.807460	+	0.589922i	$0.200841\pi$
$42$		0			0
$43$	3.62772			0.553222			0.276611	−	0.960982i	$-0.410789\pi$
$43$	3.62772			0.553222			0.276611	+	0.960982i	$0.410789\pi$
$44$		0			0
$45$	3.37228			0.502710
$46$		0			0
$47$	−2.00000			−0.291730			−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000			−0.291730			−0.145865	+	0.989305i	$0.546597\pi$
$48$		0			0
$49$	−6.05842	−	10.4935i	−0.865489	−	1.49907i
$50$		0			0
$51$	−7.37228			−1.03233
$52$		0			0
$53$	5.74456	+	9.94987i	0.789076	+	1.36672i	0.926533	+	0.376213i	$0.122774\pi$
$53$	5.74456	+	9.94987i	0.789076	+	1.36672i	−0.137457	+	0.990508i	$0.543893\pi$
$54$		0			0
$55$	3.37228	−	5.84096i	0.454718	−	0.787595i
$56$		0			0
$57$	−3.37228	−	5.84096i	−0.446670	−	0.773654i
$58$		0			0
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	0.705965	−	0.708247i	$-0.250514\pi$
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	−0.966342	+	0.257260i	$0.917180\pi$
$60$		0			0
$61$	−4.05842	+	7.02939i	−0.519628	+	0.900022i	0.480112	+	0.877207i	$0.340596\pi$
$61$	−4.05842	+	7.02939i	−0.519628	+	0.900022i	−0.999740	+	0.0228144i	$0.992737\pi$
$62$		0			0
$63$	−4.37228			−0.550856
$64$		0			0
$65$	7.37228	+	12.7692i	0.914419	+	1.58382i
$66$		0			0
$67$	−6.55842	+	11.3595i	−0.801239	+	1.38779i	0.117562	+	0.993066i	$0.462492\pi$
$67$	−6.55842	+	11.3595i	−0.801239	+	1.38779i	−0.918801	+	0.394721i	$0.870841\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−5.74456	+	9.94987i	−0.681754	+	1.18083i	0.292691	+	0.956207i	$0.405449\pi$
$71$	−5.74456	+	9.94987i	−0.681754	+	1.18083i	−0.974445	+	0.224626i	$0.927884\pi$
$72$		0			0
$73$	8.37228			0.979901			0.489951	−	0.871750i	$-0.337015\pi$
$73$	8.37228			0.979901			0.489951	+	0.871750i	$0.337015\pi$
$74$		0			0
$75$	6.37228			0.735808
$76$		0			0
$77$	−4.37228	+	7.57301i	−0.498268	+	0.863025i
$78$		0			0
$79$	−2.18614	+	3.78651i	−0.245960	+	0.426015i	−0.962401	−	0.271632i	$-0.912437\pi$
$79$	−2.18614	+	3.78651i	−0.245960	+	0.426015i	0.716441	+	0.697648i	$0.245770\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	4.00000	+	6.92820i	0.439057	+	0.760469i	0.997617	−	0.0689950i	$-0.0219793\pi$
$83$	4.00000	+	6.92820i	0.439057	+	0.760469i	−0.558560	+	0.829464i	$0.688646\pi$
$84$		0			0
$85$	−24.8614			−2.69660
$86$		0			0
$87$	0.686141	−	1.18843i	0.0735620	−	0.127413i
$88$		0			0
$89$	−4.68614	−	8.11663i	−0.496730	−	0.860361i	0.503263	−	0.864133i	$-0.332133\pi$
$89$	−4.68614	−	8.11663i	−0.496730	−	0.860361i	−0.999993	+	0.00377186i	$0.998799\pi$
$90$		0			0
$91$	−9.55842	−	16.5557i	−1.00199	−	1.73551i
$92$		0			0
$93$	−1.81386	+	3.14170i	−0.188088	+	0.325779i
$94$		0			0
$95$	−11.3723	−	19.6974i	−1.16677	−	2.02091i
$96$		0			0
$97$	−5.74456			−0.583272			−0.291636	−	0.956529i	$-0.594200\pi$
$97$	−5.74456			−0.583272			−0.291636	+	0.956529i	$0.594200\pi$
$98$		0			0
$99$	1.00000	+	1.73205i	0.100504	+	0.174078i
$100$		0			0
$101$	−14.8614			−1.47877			−0.739383	−	0.673285i	$-0.764883\pi$
$101$	−14.8614			−1.47877			−0.739383	+	0.673285i	$0.764883\pi$
$102$		0			0
$103$	−1.25544			−0.123702			−0.0618510	−	0.998085i	$-0.519700\pi$
$103$	−1.25544			−0.123702			−0.0618510	+	0.998085i	$0.519700\pi$
$104$		0			0
$105$	−14.7446			−1.43892
$106$		0			0
$107$	−3.37228	+	5.84096i	−0.326011	+	0.564667i	−0.981716	−	0.190349i	$-0.939038\pi$
$107$	−3.37228	+	5.84096i	−0.326011	+	0.564667i	0.655706	+	0.755017i	$0.272371\pi$
$108$		0			0
$109$	7.87228	+	13.6352i	0.754028	+	1.30601i	0.945856	+	0.324586i	$0.105225\pi$
$109$	7.87228	+	13.6352i	0.754028	+	1.30601i	−0.191828	+	0.981428i	$0.561442\pi$
$110$		0			0
$111$	−3.50000	+	4.97494i	−0.332205	+	0.472200i
$112$		0			0
$113$	−3.74456	−	6.48577i	−0.352259	−	0.610130i	0.634386	−	0.773016i	$-0.281253\pi$
$113$	−3.74456	−	6.48577i	−0.352259	−	0.610130i	−0.986645	+	0.162886i	$0.947920\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−4.37228			−0.404218
$118$		0			0
$119$	32.2337			2.95486
$120$		0			0
$121$	−7.00000			−0.636364
$122$		0			0
$123$	−0.686141	−	1.18843i	−0.0618672	−	0.107157i
$124$		0			0
$125$	4.62772			0.413916
$126$		0			0
$127$	7.18614	+	12.4468i	0.637667	+	1.10447i	0.985943	+	0.167080i	$0.0534337\pi$
$127$	7.18614	+	12.4468i	0.637667	+	1.10447i	−0.348277	+	0.937392i	$0.613233\pi$
$128$		0			0
$129$	−1.81386	+	3.14170i	−0.159701	+	0.276611i
$130$		0			0
$131$	−0.372281	−	0.644810i	−0.0325264	−	0.0563373i	0.849304	−	0.527904i	$-0.177022\pi$
$131$	−0.372281	−	0.644810i	−0.0325264	−	0.0563373i	−0.881830	+	0.471567i	$0.843689\pi$
$132$		0			0
$133$	14.7446	+	25.5383i	1.27852	+	2.21445i
$134$		0			0
$135$	−1.68614	+	2.92048i	−0.145120	+	0.251355i
$136$		0			0
$137$	4.62772			0.395373			0.197686	−	0.980265i	$-0.436657\pi$
$137$	4.62772			0.395373			0.197686	+	0.980265i	$0.436657\pi$
$138$		0			0
$139$	−7.18614	−	12.4468i	−0.609520	−	1.05572i	−0.991319	−	0.131475i	$-0.958029\pi$
$139$	−7.18614	−	12.4468i	−0.609520	−	1.05572i	0.381799	−	0.924245i	$-0.375305\pi$
$140$		0			0
$141$	1.00000	−	1.73205i	0.0842152	−	0.145865i
$142$		0			0
$143$	−4.37228	+	7.57301i	−0.365629	+	0.633287i
$144$		0			0
$145$	2.31386	−	4.00772i	0.192156	−	0.332823i
$146$		0			0
$147$	12.1168			0.999380
$148$		0			0
$149$	7.37228			0.603961			0.301980	−	0.953314i	$-0.402352\pi$
$149$	7.37228			0.603961			0.301980	+	0.953314i	$0.402352\pi$
$150$		0			0
$151$	−6.81386	+	11.8020i	−0.554504	+	0.960429i	0.443438	+	0.896305i	$0.353759\pi$
$151$	−6.81386	+	11.8020i	−0.554504	+	0.960429i	−0.997942	+	0.0641240i	$0.979575\pi$
$152$		0			0
$153$	3.68614	−	6.38458i	0.298007	−	0.516163i
$154$		0			0
$155$	−6.11684	+	10.5947i	−0.491317	+	0.850986i
$156$		0			0
$157$	8.24456	+	14.2800i	0.657988	+	1.13967i	0.981136	+	0.193320i	$0.0619255\pi$
$157$	8.24456	+	14.2800i	0.657988	+	1.13967i	−0.323148	+	0.946348i	$0.604741\pi$
$158$		0			0
$159$	−11.4891			−0.911147
$160$		0			0
$161$		0			0
$162$		0			0
$163$	6.62772	+	11.4795i	0.519123	+	0.899147i	0.999753	+	0.0222239i	$0.00707468\pi$
$163$	6.62772	+	11.4795i	0.519123	+	0.899147i	−0.480630	+	0.876923i	$0.659592\pi$
$164$		0			0
$165$	3.37228	+	5.84096i	0.262532	+	0.454718i
$166$		0			0
$167$	10.7446	−	18.6101i	0.831439	−	1.44009i	−0.0654577	−	0.997855i	$-0.520851\pi$
$167$	10.7446	−	18.6101i	0.831439	−	1.44009i	0.896897	−	0.442240i	$-0.145816\pi$
$168$		0			0
$169$	−3.05842	−	5.29734i	−0.235263	−	0.407488i
$170$		0			0
$171$	6.74456			0.515770
$172$		0			0
$173$	−2.94158	−	5.09496i	−0.223644	−	0.387363i	0.732268	−	0.681017i	$-0.238462\pi$
$173$	−2.94158	−	5.09496i	−0.223644	−	0.387363i	−0.955912	+	0.293654i	$0.905129\pi$
$174$		0			0
$175$	−27.8614			−2.10612
$176$		0			0
$177$	4.00000			0.300658
$178$		0			0
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	7.87228	−	13.6352i	0.585142	−	1.01350i	−0.409716	−	0.912213i	$-0.634372\pi$
$181$	7.87228	−	13.6352i	0.585142	−	1.01350i	0.994858	−	0.101282i	$-0.0322946\pi$
$182$		0			0
$183$	−4.05842	−	7.02939i	−0.300007	−	0.519628i
$184$		0			0
$185$	−11.8030	+	16.7769i	−0.867773	+	1.23346i
$186$		0			0
$187$	−7.37228	−	12.7692i	−0.539115	−	0.933774i
$188$		0			0
$189$	2.18614	−	3.78651i	0.159018	−	0.275428i
$190$		0			0
$191$	11.2554			0.814415			0.407207	−	0.913336i	$-0.366503\pi$
$191$	11.2554			0.814415			0.407207	+	0.913336i	$0.366503\pi$
$192$		0			0
$193$	4.48913			0.323134			0.161567	−	0.986862i	$-0.448345\pi$
$193$	4.48913			0.323134			0.161567	+	0.986862i	$0.448345\pi$
$194$		0			0
$195$	−14.7446			−1.05588
$196$		0			0
$197$	−9.68614	−	16.7769i	−0.690109	−	1.19530i	−0.971802	−	0.235799i	$-0.924229\pi$
$197$	−9.68614	−	16.7769i	−0.690109	−	1.19530i	0.281693	−	0.959505i	$-0.409104\pi$
$198$		0			0
$199$	12.3723			0.877048			0.438524	−	0.898720i	$-0.355501\pi$
$199$	12.3723			0.877048			0.438524	+	0.898720i	$0.355501\pi$
$200$		0			0
$201$	−6.55842	−	11.3595i	−0.462595	−	0.801239i
$202$		0			0
$203$	−3.00000	+	5.19615i	−0.210559	+	0.364698i
$204$		0			0
$205$	−2.31386	−	4.00772i	−0.161607	−	0.279911i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	6.74456	−	11.6819i	0.466531	−	0.808056i
$210$		0			0
$211$	−7.62772			−0.525114			−0.262557	−	0.964917i	$-0.584566\pi$
$211$	−7.62772			−0.525114			−0.262557	+	0.964917i	$0.584566\pi$
$212$		0			0
$213$	−5.74456	−	9.94987i	−0.393611	−	0.681754i
$214$		0			0
$215$	−6.11684	+	10.5947i	−0.417165	+	0.722551i
$216$		0			0
$217$	7.93070	−	13.7364i	0.538371	−	0.932486i
$218$		0			0
$219$	−4.18614	+	7.25061i	−0.282873	+	0.489951i
$220$		0			0
$221$	32.2337			2.16827
$222$		0			0
$223$	−0.883156			−0.0591405			−0.0295703	−	0.999563i	$-0.509414\pi$
$223$	−0.883156			−0.0591405			−0.0295703	+	0.999563i	$0.509414\pi$
$224$		0			0
$225$	−3.18614	+	5.51856i	−0.212409	+	0.367904i
$226$		0			0
$227$	5.74456	−	9.94987i	0.381280	−	0.660396i	−0.609965	−	0.792428i	$-0.708817\pi$
$227$	5.74456	−	9.94987i	0.381280	−	0.660396i	0.991246	+	0.132032i	$0.0421500\pi$
$228$		0			0
$229$	1.12772	−	1.95327i	0.0745217	−	0.129075i	−0.826356	−	0.563147i	$-0.809590\pi$
$229$	1.12772	−	1.95327i	0.0745217	−	0.129075i	0.900878	+	0.434072i	$0.142924\pi$
$230$		0			0
$231$	−4.37228	−	7.57301i	−0.287675	−	0.498268i
$232$		0			0
$233$	11.6060			0.760332			0.380166	−	0.924918i	$-0.375867\pi$
$233$	11.6060			0.760332			0.380166	+	0.924918i	$0.375867\pi$
$234$		0			0
$235$	3.37228	−	5.84096i	0.219983	−	0.381022i
$236$		0			0
$237$	−2.18614	−	3.78651i	−0.142005	−	0.245960i
$238$		0			0
$239$	6.11684	+	10.5947i	0.395666	+	0.685313i	0.993186	−	0.116541i	$-0.0371805\pi$
$239$	6.11684	+	10.5947i	0.395666	+	0.685313i	−0.597520	+	0.801854i	$0.703847\pi$
$240$		0			0
$241$	−3.44158	+	5.96099i	−0.221692	+	0.383981i	−0.955322	−	0.295568i	$-0.904491\pi$
$241$	−3.44158	+	5.96099i	−0.221692	+	0.383981i	0.733630	+	0.679549i	$0.237824\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	40.8614			2.61054
$246$		0			0
$247$	14.7446	+	25.5383i	0.938174	+	1.62497i
$248$		0			0
$249$	−8.00000			−0.506979
$250$		0			0
$251$	1.25544			0.0792425			0.0396213	−	0.999215i	$-0.487385\pi$
$251$	1.25544			0.0792425			0.0396213	+	0.999215i	$0.487385\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	12.4307	−	21.5306i	0.778441	−	1.34830i
$256$		0			0
$257$	4.43070	+	7.67420i	0.276380	+	0.478704i	0.970482	−	0.241172i	$-0.0775319\pi$
$257$	4.43070	+	7.67420i	0.276380	+	0.478704i	−0.694103	+	0.719876i	$0.744199\pi$
$258$		0			0
$259$	15.3030	−	21.7518i	0.950881	−	1.35159i
$260$		0			0
$261$	0.686141	+	1.18843i	0.0424710	+	0.0735620i
$262$		0			0
$263$	−7.62772	+	13.2116i	−0.470345	+	0.814662i	−0.999425	−	0.0339103i	$-0.989204\pi$
$263$	−7.62772	+	13.2116i	−0.470345	+	0.814662i	0.529080	+	0.848572i	$0.322537\pi$
$264$		0			0
$265$	−38.7446			−2.38006
$266$		0			0
$267$	9.37228			0.573574
$268$		0			0
$269$	2.00000			0.121942			0.0609711	−	0.998140i	$-0.480580\pi$
$269$	2.00000			0.121942			0.0609711	+	0.998140i	$0.480580\pi$
$270$		0			0
$271$	−4.93070	−	8.54023i	−0.299519	−	0.518782i	0.676507	−	0.736436i	$-0.263493\pi$
$271$	−4.93070	−	8.54023i	−0.299519	−	0.518782i	−0.976026	+	0.217654i	$0.930159\pi$
$272$		0			0
$273$	19.1168			1.15700
$274$		0			0
$275$	6.37228	+	11.0371i	0.384263	+	0.665563i
$276$		0			0
$277$	15.4307	−	26.7268i	0.927141	−	1.60586i	0.139060	−	0.990284i	$-0.455592\pi$
$277$	15.4307	−	26.7268i	0.927141	−	1.60586i	0.788081	−	0.615572i	$-0.211075\pi$
$278$		0			0
$279$	−1.81386	−	3.14170i	−0.108593	−	0.188088i
$280$		0			0
$281$	−5.05842	−	8.76144i	−0.301760	−	0.522664i	0.674775	−	0.738024i	$-0.264241\pi$
$281$	−5.05842	−	8.76144i	−0.301760	−	0.522664i	−0.976535	+	0.215360i	$0.930908\pi$
$282$		0			0
$283$	8.55842	−	14.8236i	0.508745	−	0.881173i	−0.491203	−	0.871045i	$-0.663443\pi$
$283$	8.55842	−	14.8236i	0.508745	−	0.881173i	0.999949	−	0.0101279i	$-0.00322387\pi$
$284$		0			0
$285$	22.7446			1.34727
$286$		0			0
$287$	3.00000	+	5.19615i	0.177084	+	0.306719i
$288$		0			0
$289$	−18.6753	+	32.3465i	−1.09855	+	1.90274i
$290$		0			0
$291$	2.87228	−	4.97494i	0.168376	−	0.291636i
$292$		0			0
$293$	7.94158	−	13.7552i	0.463952	−	0.803588i	−0.535202	−	0.844724i	$-0.679764\pi$
$293$	7.94158	−	13.7552i	0.463952	−	0.803588i	0.999154	+	0.0411360i	$0.0130977\pi$
$294$		0			0
$295$	13.4891			0.785367
$296$		0			0
$297$	−2.00000			−0.116052
$298$		0			0
$299$		0			0
$300$		0			0
$301$	7.93070	−	13.7364i	0.457118	−	0.791752i
$302$		0			0
$303$	7.43070	−	12.8704i	0.426883	−	0.739383i
$304$		0			0
$305$	−13.6861	−	23.7051i	−0.783666	−	1.35735i
$306$		0			0
$307$	−9.11684			−0.520326			−0.260163	−	0.965565i	$-0.583776\pi$
$307$	−9.11684			−0.520326			−0.260163	+	0.965565i	$0.583776\pi$
$308$		0			0
$309$	0.627719	−	1.08724i	0.0357097	−	0.0618510i
$310$		0			0
$311$	8.48913	+	14.7036i	0.481374	+	0.833764i	0.999772	−	0.0213754i	$-0.00680452\pi$
$311$	8.48913	+	14.7036i	0.481374	+	0.833764i	−0.518397	+	0.855140i	$0.673471\pi$
$312$		0			0
$313$	8.50000	+	14.7224i	0.480448	+	0.832161i	0.999748	−	0.0224310i	$-0.00714060\pi$
$313$	8.50000	+	14.7224i	0.480448	+	0.832161i	−0.519300	+	0.854592i	$0.673807\pi$
$314$		0			0
$315$	7.37228	−	12.7692i	0.415381	−	0.719461i
$316$		0			0
$317$	15.0584	+	26.0820i	0.845765	+	1.46491i	0.884955	+	0.465677i	$0.154189\pi$
$317$	15.0584	+	26.0820i	0.845765	+	1.46491i	−0.0391897	+	0.999232i	$0.512478\pi$
$318$		0			0
$319$	2.74456			0.153666
$320$		0			0
$321$	−3.37228	−	5.84096i	−0.188222	−	0.326011i
$322$		0			0
$323$	−49.7228			−2.76665
$324$		0			0
$325$	−27.8614			−1.54547
$326$		0			0
$327$	−15.7446			−0.870676
$328$		0			0
$329$	−4.37228	+	7.57301i	−0.241052	+	0.417514i
$330$		0			0
$331$	2.30298	+	3.98889i	0.126583	+	0.219249i	0.922351	−	0.386353i	$-0.126266\pi$
$331$	2.30298	+	3.98889i	0.126583	+	0.219249i	−0.795767	+	0.605602i	$0.792932\pi$
$332$		0			0
$333$	−2.55842	−	5.51856i	−0.140201	−	0.302415i
$334$		0			0
$335$	−22.1168	−	38.3075i	−1.20837	−	2.09296i
$336$		0			0
$337$	−9.12772	+	15.8097i	−0.497219	+	0.861208i	−0.999995	−	0.00320880i	$-0.998979\pi$
$337$	−9.12772	+	15.8097i	−0.497219	+	0.861208i	0.502776	+	0.864417i	$0.332312\pi$
$338$		0			0
$339$	7.48913			0.406753
$340$		0			0
$341$	−7.25544			−0.392904
$342$		0			0
$343$	−22.3723			−1.20799
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−15.2554			−0.818955			−0.409477	−	0.912320i	$-0.634289\pi$
$347$	−15.2554			−0.818955			−0.409477	+	0.912320i	$0.634289\pi$
$348$		0			0
$349$	−4.05842	−	7.02939i	−0.217242	−	0.376275i	0.736722	−	0.676196i	$-0.236373\pi$
$349$	−4.05842	−	7.02939i	−0.217242	−	0.376275i	−0.953964	+	0.299921i	$0.903040\pi$
$350$		0			0
$351$	2.18614	−	3.78651i	0.116688	−	0.202109i
$352$		0			0
$353$	4.80298	+	8.31901i	0.255637	+	0.442776i	0.965068	−	0.261998i	$-0.0843815\pi$
$353$	4.80298	+	8.31901i	0.255637	+	0.442776i	−0.709431	+	0.704775i	$0.751048\pi$
$354$		0			0
$355$	−19.3723	−	33.5538i	−1.02817	−	1.78085i
$356$		0			0
$357$	−16.1168	+	27.9152i	−0.852994	+	1.47743i
$358$		0			0
$359$	22.2337			1.17345			0.586725	−	0.809787i	$-0.300417\pi$
$359$	22.2337			1.17345			0.586725	+	0.809787i	$0.300417\pi$
$360$		0			0
$361$	−13.2446	−	22.9403i	−0.697082	−	1.20738i
$362$		0			0
$363$	3.50000	−	6.06218i	0.183702	−	0.318182i
$364$		0			0
$365$	−14.1168	+	24.4511i	−0.738909	+	1.27983i
$366$		0			0
$367$	−5.55842	+	9.62747i	−0.290147	+	0.502550i	−0.973844	−	0.227216i	$-0.927038\pi$
$367$	−5.55842	+	9.62747i	−0.290147	+	0.502550i	0.683697	+	0.729766i	$0.260371\pi$
$368$		0			0
$369$	1.37228			0.0714381
$370$		0			0
$371$	50.2337			2.60800
$372$		0			0
$373$	15.5000	−	26.8468i	0.802560	−	1.39007i	−0.115367	−	0.993323i	$-0.536804\pi$
$373$	15.5000	−	26.8468i	0.802560	−	1.39007i	0.917926	−	0.396751i	$-0.129862\pi$
$374$		0			0
$375$	−2.31386	+	4.00772i	−0.119487	+	0.206958i
$376$		0			0
$377$	−3.00000	+	5.19615i	−0.154508	+	0.267615i
$378$		0			0
$379$	14.8614	+	25.7407i	0.763379	+	1.32221i	0.941099	+	0.338130i	$0.109795\pi$
$379$	14.8614	+	25.7407i	0.763379	+	1.32221i	−0.177720	+	0.984081i	$0.556872\pi$
$380$		0			0
$381$	−14.3723			−0.736314
$382$		0			0
$383$	14.1168	−	24.4511i	0.721337	−	1.24939i	−0.239127	−	0.970988i	$-0.576861\pi$
$383$	14.1168	−	24.4511i	0.721337	−	1.24939i	0.960464	−	0.278404i	$-0.0898054\pi$
$384$		0			0
$385$	−14.7446	−	25.5383i	−0.751452	−	1.30155i
$386$		0			0
$387$	−1.81386	−	3.14170i	−0.0922037	−	0.159701i
$388$		0			0
$389$	−12.0584	+	20.8858i	−0.611386	+	1.05895i	0.379621	+	0.925142i	$0.376054\pi$
$389$	−12.0584	+	20.8858i	−0.611386	+	1.05895i	−0.991007	+	0.133810i	$0.957279\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	0.744563			0.0375582
$394$		0			0
$395$	−7.37228	−	12.7692i	−0.370940	−	0.642486i
$396$		0			0
$397$	−19.0000			−0.953583			−0.476791	−	0.879017i	$-0.658200\pi$
$397$	−19.0000			−0.953583			−0.476791	+	0.879017i	$0.658200\pi$
$398$		0			0
$399$	−29.4891			−1.47630
$400$		0			0
$401$	−14.7446			−0.736308			−0.368154	−	0.929765i	$-0.620010\pi$
$401$	−14.7446			−0.736308			−0.368154	+	0.929765i	$0.620010\pi$
$402$		0			0
$403$	7.93070	−	13.7364i	0.395056	−	0.684258i
$404$		0			0
$405$	−1.68614	−	2.92048i	−0.0837850	−	0.145120i
$406$		0			0
$407$	−12.1168	−	1.08724i	−0.600610	−	0.0538925i
$408$		0			0
$409$	6.12772	+	10.6135i	0.302996	+	0.524805i	0.976813	−	0.214093i	$-0.0686797\pi$
$409$	6.12772	+	10.6135i	0.302996	+	0.524805i	−0.673817	+	0.738898i	$0.735346\pi$
$410$		0			0
$411$	−2.31386	+	4.00772i	−0.114134	+	0.197686i
$412$		0			0
$413$	−17.4891			−0.860584
$414$		0			0
$415$	−26.9783			−1.32431
$416$		0			0
$417$	14.3723			0.703814
$418$		0			0
$419$	−1.74456	−	3.02167i	−0.0852275	−	0.147618i	0.820261	−	0.571990i	$-0.193828\pi$
$419$	−1.74456	−	3.02167i	−0.0852275	−	0.147618i	−0.905488	+	0.424372i	$0.860495\pi$
$420$		0			0
$421$	−17.3723			−0.846673			−0.423337	−	0.905972i	$-0.639141\pi$
$421$	−17.3723			−0.846673			−0.423337	+	0.905972i	$0.639141\pi$
$422$		0			0
$423$	1.00000	+	1.73205i	0.0486217	+	0.0842152i
$424$		0			0
$425$	23.4891	−	40.6844i	1.13939	−	1.97348i
$426$		0			0
$427$	17.7446	+	30.7345i	0.858720	+	1.48735i
$428$		0			0
$429$	−4.37228	−	7.57301i	−0.211096	−	0.365629i
$430$		0			0
$431$	−18.4891	+	32.0241i	−0.890590	+	1.54255i	−0.0514202	+	0.998677i	$0.516375\pi$
$431$	−18.4891	+	32.0241i	−0.890590	+	1.54255i	−0.839170	+	0.543870i	$0.816959\pi$
$432$		0			0
$433$	13.3723			0.642631			0.321315	−	0.946972i	$-0.395875\pi$
$433$	13.3723			0.642631			0.321315	+	0.946972i	$0.395875\pi$
$434$		0			0
$435$	2.31386	+	4.00772i	0.110941	+	0.192156i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	7.18614	−	12.4468i	0.342976	−	0.594051i	−0.642008	−	0.766698i	$-0.721898\pi$
$439$	7.18614	−	12.4468i	0.342976	−	0.594051i	0.984984	+	0.172646i	$0.0552318\pi$
$440$		0			0
$441$	−6.05842	+	10.4935i	−0.288496	+	0.499690i
$442$		0			0
$443$	−17.4891			−0.830933			−0.415467	−	0.909608i	$-0.636382\pi$
$443$	−17.4891			−0.830933			−0.415467	+	0.909608i	$0.636382\pi$
$444$		0			0
$445$	31.6060			1.49827
$446$		0			0
$447$	−3.68614	+	6.38458i	−0.174348	+	0.301980i
$448$		0			0
$449$	10.4891	−	18.1677i	0.495012	−	0.857387i	−0.504971	−	0.863136i	$-0.668497\pi$
$449$	10.4891	−	18.1677i	0.495012	−	0.857387i	0.999983	+	0.00574961i	$0.00183017\pi$
$450$		0			0
$451$	1.37228	−	2.37686i	0.0646182	−	0.111922i
$452$		0			0
$453$	−6.81386	−	11.8020i	−0.320143	−	0.554504i
$454$		0			0
$455$	64.4674			3.02228
$456$		0			0
$457$	19.5475	−	33.8573i	0.914396	−	1.58378i	0.106612	−	0.994301i	$-0.466000\pi$
$457$	19.5475	−	33.8573i	0.914396	−	1.58378i	0.807784	−	0.589479i	$-0.200667\pi$
$458$		0			0
$459$	3.68614	+	6.38458i	0.172054	+	0.298007i
$460$		0			0
$461$	−12.4891	−	21.6318i	−0.581677	−	1.00749i	−0.995281	−	0.0970366i	$-0.969064\pi$
$461$	−12.4891	−	21.6318i	−0.581677	−	1.00749i	0.413604	−	0.910457i	$-0.364270\pi$
$462$		0			0
$463$	8.55842	−	14.8236i	0.397744	−	0.688912i	−0.595704	−	0.803204i	$-0.703127\pi$
$463$	8.55842	−	14.8236i	0.397744	−	0.688912i	0.993447	+	0.114292i	$0.0364600\pi$
$464$		0			0
$465$	−6.11684	−	10.5947i	−0.283662	−	0.491317i
$466$		0			0
$467$	−3.25544			−0.150644			−0.0753218	−	0.997159i	$-0.523998\pi$
$467$	−3.25544			−0.150644			−0.0753218	+	0.997159i	$0.523998\pi$
$468$		0			0
$469$	28.6753	+	49.6670i	1.32410	+	2.29341i
$470$		0			0
$471$	−16.4891			−0.759779
$472$		0			0
$473$	−7.25544			−0.333605
$474$		0			0
$475$	42.9783			1.97198
$476$		0			0
$477$	5.74456	−	9.94987i	0.263025	−	0.455573i
$478$		0			0
$479$	17.1168	+	29.6472i	0.782089	+	1.35462i	0.930723	+	0.365725i	$0.119179\pi$
$479$	17.1168	+	29.6472i	0.782089	+	1.35462i	−0.148634	+	0.988892i	$0.547488\pi$
$480$		0			0
$481$	15.3030	−	21.7518i	0.697756	−	0.991798i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	9.68614	−	16.7769i	0.439825	−	0.761799i
$486$		0			0
$487$	14.5109			0.657550			0.328775	−	0.944408i	$-0.393364\pi$
$487$	14.5109			0.657550			0.328775	+	0.944408i	$0.393364\pi$
$488$		0			0
$489$	−13.2554			−0.599432
$490$		0			0
$491$	−6.00000			−0.270776			−0.135388	−	0.990793i	$-0.543228\pi$
$491$	−6.00000			−0.270776			−0.135388	+	0.990793i	$0.543228\pi$
$492$		0			0
$493$	−5.05842	−	8.76144i	−0.227820	−	0.394596i
$494$		0			0
$495$	−6.74456			−0.303146
$496$		0			0
$497$	25.1168	+	43.5036i	1.12664	+	1.95141i
$498$		0			0
$499$	4.11684	−	7.13058i	0.184295	−	0.319209i	−0.759044	−	0.651040i	$-0.774333\pi$
$499$	4.11684	−	7.13058i	0.184295	−	0.319209i	0.943339	+	0.331831i	$0.107666\pi$
$500$		0			0
$501$	10.7446	+	18.6101i	0.480032	+	0.831439i
$502$		0			0
$503$	−11.0000	−	19.0526i	−0.490466	−	0.849512i	0.509474	−	0.860486i	$-0.329840\pi$
$503$	−11.0000	−	19.0526i	−0.490466	−	0.849512i	−0.999940	+	0.0109744i	$0.996507\pi$
$504$		0			0
$505$	25.0584	−	43.4025i	1.11509	−	1.93138i
$506$		0			0
$507$	6.11684			0.271659
$508$		0			0
$509$	0.686141	+	1.18843i	0.0304127	+	0.0526763i	0.880831	−	0.473431i	$-0.156985\pi$
$509$	0.686141	+	1.18843i	0.0304127	+	0.0526763i	−0.850418	+	0.526107i	$0.823651\pi$
$510$		0			0
$511$	18.3030	−	31.7017i	0.809676	−	1.40240i
$512$		0			0
$513$	−3.37228	+	5.84096i	−0.148890	+	0.257885i
$514$		0			0
$515$	2.11684	−	3.66648i	0.0932793	−	0.161564i
$516$		0			0
$517$	4.00000			0.175920
$518$		0			0
$519$	5.88316			0.258242
$520$		0			0
$521$	−4.62772	+	8.01544i	−0.202744	+	0.351163i	−0.949412	−	0.314034i	$-0.898319\pi$
$521$	−4.62772	+	8.01544i	−0.202744	+	0.351163i	0.746668	+	0.665197i	$0.231653\pi$
$522$		0			0
$523$	9.55842	−	16.5557i	0.417961	−	0.723929i	−0.577774	−	0.816197i	$-0.696078\pi$
$523$	9.55842	−	16.5557i	0.417961	−	0.723929i	0.995734	+	0.0922681i	$0.0294117\pi$
$524$		0			0
$525$	13.9307	−	24.1287i	0.607986	−	1.05306i
$526$		0			0
$527$	13.3723	+	23.1615i	0.582506	+	1.00893i
$528$		0			0
$529$	−23.0000			−1.00000
$530$		0			0
$531$	−2.00000	+	3.46410i	−0.0867926	+	0.150329i
$532$		0			0
$533$	3.00000	+	5.19615i	0.129944	+	0.225070i
$534$		0			0
$535$	−11.3723	−	19.6974i	−0.491667	−	0.851592i
$536$		0			0
$537$	−6.00000	+	10.3923i	−0.258919	+	0.448461i
$538$		0			0
$539$	12.1168	+	20.9870i	0.521909	+	0.903974i
$540$		0			0
$541$	5.74456			0.246978			0.123489	−	0.992346i	$-0.460592\pi$
$541$	5.74456			0.246978			0.123489	+	0.992346i	$0.460592\pi$
$542$		0			0
$543$	7.87228	+	13.6352i	0.337832	+	0.585142i
$544$		0			0
$545$	−53.0951			−2.27434
$546$		0			0
$547$	−24.0951			−1.03023			−0.515116	−	0.857121i	$-0.672251\pi$
$547$	−24.0951			−1.03023			−0.515116	+	0.857121i	$0.672251\pi$
$548$		0			0
$549$	8.11684			0.346418
$550$		0			0
$551$	4.62772	−	8.01544i	0.197147	−	0.341469i
$552$		0			0
$553$	9.55842	+	16.5557i	0.406465	+	0.704019i
$554$		0			0
$555$	−8.62772	−	18.6101i	−0.366226	−	0.789956i
$556$		0			0
$557$	7.05842	+	12.2255i	0.299075	+	0.518013i	0.975925	−	0.218108i	$-0.0699886\pi$
$557$	7.05842	+	12.2255i	0.299075	+	0.518013i	−0.676850	+	0.736121i	$0.736655\pi$
$558$		0			0
$559$	7.93070	−	13.7364i	0.335433	−	0.580987i
$560$		0			0
$561$	14.7446			0.622516
$562$		0			0
$563$	−24.7446			−1.04286			−0.521429	−	0.853294i	$-0.674601\pi$
$563$	−24.7446			−1.04286			−0.521429	+	0.853294i	$0.674601\pi$
$564$		0			0
$565$	25.2554			1.06250
$566$		0			0
$567$	2.18614	+	3.78651i	0.0918093	+	0.159018i
$568$		0			0
$569$	21.3723			0.895973			0.447986	−	0.894040i	$-0.352141\pi$
$569$	21.3723			0.895973			0.447986	+	0.894040i	$0.352141\pi$
$570$		0			0
$571$	−19.4198	−	33.6361i	−0.812695	−	1.40763i	−0.910972	−	0.412469i	$-0.864666\pi$
$571$	−19.4198	−	33.6361i	−0.812695	−	1.40763i	0.0982770	−	0.995159i	$-0.468667\pi$
$572$		0			0
$573$	−5.62772	+	9.74749i	−0.235101	+	0.407207i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−16.4891	−	28.5600i	−0.686451	−	1.18897i	−0.972978	−	0.230896i	$-0.925834\pi$
$577$	−16.4891	−	28.5600i	−0.686451	−	1.18897i	0.286527	−	0.958072i	$-0.407499\pi$
$578$		0			0
$579$	−2.24456	+	3.88770i	−0.0932808	+	0.161567i
$580$		0			0
$581$	34.9783			1.45114
$582$		0			0
$583$	−11.4891	−	19.8997i	−0.475831	−	0.824163i
$584$		0			0
$585$	7.37228	−	12.7692i	0.304806	−	0.527940i
$586$		0			0
$587$	4.37228	−	7.57301i	0.180463	−	0.312572i	−0.761575	−	0.648077i	$-0.775574\pi$
$587$	4.37228	−	7.57301i	0.180463	−	0.312572i	0.942038	+	0.335505i	$0.108907\pi$
$588$		0			0
$589$	−12.2337	+	21.1894i	−0.504080	+	0.873093i
$590$		0			0
$591$	19.3723			0.796869
$592$		0			0
$593$	8.62772			0.354298			0.177149	−	0.984184i	$-0.443313\pi$
$593$	8.62772			0.354298			0.177149	+	0.984184i	$0.443313\pi$
$594$		0			0
$595$	−54.3505	+	94.1379i	−2.22815	+	3.85928i
$596$		0			0
$597$	−6.18614	+	10.7147i	−0.253182	+	0.438524i
$598$		0			0
$599$	9.37228	−	16.2333i	0.382941	−	0.663273i	−0.608540	−	0.793523i	$-0.708245\pi$
$599$	9.37228	−	16.2333i	0.382941	−	0.663273i	0.991481	+	0.130250i	$0.0415779\pi$
$600$		0			0
$601$	8.50000	+	14.7224i	0.346722	+	0.600541i	0.985665	−	0.168714i	$-0.0539613\pi$
$601$	8.50000	+	14.7224i	0.346722	+	0.600541i	−0.638943	+	0.769254i	$0.720628\pi$
$602$		0			0
$603$	13.1168			0.534159
$604$		0			0
$605$	11.8030	−	20.4434i	0.479860	−	0.831141i
$606$		0			0
$607$	−4.86141	−	8.42020i	−0.197318	−	0.341766i	0.750340	−	0.661052i	$-0.229890\pi$
$607$	−4.86141	−	8.42020i	−0.197318	−	0.341766i	−0.947658	+	0.319287i	$0.896557\pi$
$608$		0			0
$609$	−3.00000	−	5.19615i	−0.121566	−	0.210559i
$610$		0			0
$611$	−4.37228	+	7.57301i	−0.176884	+	0.306371i
$612$		0			0
$613$	5.43070	+	9.40625i	0.219344	+	0.379915i	0.954608	−	0.297866i	$-0.0962750\pi$
$613$	5.43070	+	9.40625i	0.219344	+	0.379915i	−0.735264	+	0.677781i	$0.762942\pi$
$614$		0			0
$615$	4.62772			0.186608
$616$		0			0
$617$	−16.8614	−	29.2048i	−0.678815	−	1.17574i	−0.975338	−	0.220716i	$-0.929161\pi$
$617$	−16.8614	−	29.2048i	−0.678815	−	1.17574i	0.296523	−	0.955026i	$-0.404173\pi$
$618$		0			0
$619$	40.8397			1.64148			0.820742	−	0.571299i	$-0.193560\pi$
$619$	40.8397			1.64148			0.820742	+	0.571299i	$0.193560\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−40.9783			−1.64176
$624$		0			0
$625$	8.12772	−	14.0776i	0.325109	−	0.563105i
$626$		0			0
$627$	6.74456	+	11.6819i	0.269352	+	0.466531i
$628$		0			0
$629$	18.8614	+	40.6844i	0.752054	+	1.62219i
$630$		0			0
$631$	−12.4416	−	21.5494i	−0.495291	−	0.857870i	0.504694	−	0.863298i	$-0.331605\pi$
$631$	−12.4416	−	21.5494i	−0.495291	−	0.857870i	−0.999985	+	0.00542852i	$0.998272\pi$
$632$		0			0
$633$	3.81386	−	6.60580i	0.151587	−	0.262557i
$634$		0			0
$635$	−48.4674			−1.92337
$636$		0			0
$637$	−52.9783			−2.09907
$638$		0			0
$639$	11.4891			0.454503
$640$		0			0
$641$	−1.05842	−	1.83324i	−0.0418052	−	0.0724087i	0.844366	−	0.535767i	$-0.179978\pi$
$641$	−1.05842	−	1.83324i	−0.0418052	−	0.0724087i	−0.886171	+	0.463359i	$0.846644\pi$
$642$		0			0
$643$	22.6060			0.891492			0.445746	−	0.895159i	$-0.352938\pi$
$643$	22.6060			0.891492			0.445746	+	0.895159i	$0.352938\pi$
$644$		0			0
$645$	−6.11684	−	10.5947i	−0.240850	−	0.417165i
$646$		0			0
$647$	8.86141	−	15.3484i	0.348378	−	0.603408i	−0.637584	−	0.770381i	$-0.720066\pi$
$647$	8.86141	−	15.3484i	0.348378	−	0.603408i	0.985961	+	0.166973i	$0.0533993\pi$
$648$		0			0
$649$	4.00000	+	6.92820i	0.157014	+	0.271956i
$650$		0			0
$651$	7.93070	+	13.7364i	0.310829	+	0.538371i
$652$		0			0
$653$	−23.9198	+	41.4304i	−0.936055	+	1.62130i	−0.163314	+	0.986574i	$0.552218\pi$
$653$	−23.9198	+	41.4304i	−0.936055	+	1.62130i	−0.772741	+	0.634721i	$0.781115\pi$
$654$		0			0
$655$	2.51087			0.0981080
$656$		0			0
$657$	−4.18614	−	7.25061i	−0.163317	−	0.282873i
$658$		0			0
$659$	21.1168	−	36.5754i	0.822595	−	1.42478i	−0.0811477	−	0.996702i	$-0.525859\pi$
$659$	21.1168	−	36.5754i	0.822595	−	1.42478i	0.903743	−	0.428075i	$-0.140808\pi$
$660$		0			0
$661$	12.9891	−	22.4978i	0.505218	−	0.875064i	−0.494763	−	0.869028i	$-0.664745\pi$
$661$	12.9891	−	22.4978i	0.505218	−	0.875064i	0.999982	−	0.00603623i	$-0.00192140\pi$
$662$		0			0
$663$	−16.1168	+	27.9152i	−0.625926	+	1.08414i
$664$		0			0
$665$	−99.4456			−3.85634
$666$		0			0
$667$		0			0
$668$		0			0
$669$	0.441578	−	0.764836i	0.0170724	−	0.0295703i
$670$		0			0
$671$	8.11684	−	14.0588i	0.313347	−	0.542733i
$672$		0			0
$673$	−16.4891	+	28.5600i	−0.635609	+	1.10091i	0.350777	+	0.936459i	$0.385918\pi$
$673$	−16.4891	+	28.5600i	−0.635609	+	1.10091i	−0.986386	+	0.164448i	$0.947416\pi$
$674$		0			0
$675$	−3.18614	−	5.51856i	−0.122635	−	0.212409i
$676$		0			0
$677$	−11.8832			−0.456707			−0.228353	−	0.973578i	$-0.573334\pi$
$677$	−11.8832			−0.456707			−0.228353	+	0.973578i	$0.573334\pi$
$678$		0			0
$679$	−12.5584	+	21.7518i	−0.481948	+	0.834758i
$680$		0			0
$681$	5.74456	+	9.94987i	0.220132	+	0.381280i
$682$		0			0
$683$	−10.1168	−	17.5229i	−0.387110	−	0.670495i	0.604949	−	0.796264i	$-0.293193\pi$
$683$	−10.1168	−	17.5229i	−0.387110	−	0.670495i	−0.992060	+	0.125769i	$0.959860\pi$
$684$		0			0
$685$	−7.80298	+	13.5152i	−0.298137	+	0.516388i
$686$		0			0
$687$	1.12772	+	1.95327i	0.0430252	+	0.0745217i
$688$		0			0
$689$	50.2337			1.91375
$690$		0			0
$691$	−10.1861	−	17.6429i	−0.387499	−	0.671168i	0.604613	−	0.796519i	$-0.293328\pi$
$691$	−10.1861	−	17.6429i	−0.387499	−	0.671168i	−0.992112	+	0.125351i	$0.959994\pi$
$692$		0			0
$693$	8.74456			0.332178
$694$		0			0
$695$	48.4674			1.83847
$696$		0			0
$697$	−10.1168			−0.383203
$698$		0			0
$699$	−5.80298	+	10.0511i	−0.219489	+	0.380166i
$700$		0			0
$701$	−3.88316	−	6.72582i	−0.146665	−	0.254031i	0.783328	−	0.621609i	$-0.213521\pi$
$701$	−3.88316	−	6.72582i	−0.146665	−	0.254031i	−0.929993	+	0.367578i	$0.880187\pi$
$702$		0			0
$703$	−23.6060	+	33.5538i	−0.890316	+	1.26550i
$704$		0			0
$705$	3.37228	+	5.84096i	0.127007	+	0.219983i
$706$		0			0
$707$	−32.4891	+	56.2728i	−1.22188	+	2.11636i
$708$		0			0
$709$	18.6060			0.698762			0.349381	−	0.936981i	$-0.386392\pi$
$709$	18.6060			0.698762			0.349381	+	0.936981i	$0.386392\pi$
$710$		0			0
$711$	4.37228			0.163973
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−14.7446	−	25.5383i	−0.551415	−	0.955079i
$716$		0			0
$717$	−12.2337			−0.456875
$718$		0			0
$719$	18.6060	+	32.2265i	0.693886	+	1.20185i	0.970555	+	0.240880i	$0.0774360\pi$
$719$	18.6060	+	32.2265i	0.693886	+	1.20185i	−0.276669	+	0.960965i	$0.589231\pi$
$720$		0			0
$721$	−2.74456	+	4.75372i	−0.102213	+	0.177038i
$722$		0			0
$723$	−3.44158	−	5.96099i	−0.127994	−	0.221692i
$724$		0			0
$725$	4.37228	+	7.57301i	0.162382	+	0.281255i
$726$		0			0
$727$	−17.0475	+	29.5272i	−0.632259	+	1.09510i	0.354830	+	0.934931i	$0.384539\pi$
$727$	−17.0475	+	29.5272i	−0.632259	+	1.09510i	−0.987089	+	0.160173i	$0.948795\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	13.3723	+	23.1615i	0.494592	+	0.856658i
$732$		0			0
$733$	−1.81386	+	3.14170i	−0.0669964	+	0.116041i	−0.897578	−	0.440856i	$-0.854675\pi$
$733$	−1.81386	+	3.14170i	−0.0669964	+	0.116041i	0.830581	+	0.556897i	$0.188008\pi$
$734$		0			0
$735$	−20.4307	+	35.3870i	−0.753598	+	1.30527i
$736$		0			0
$737$	13.1168	−	22.7190i	0.483165	−	0.836867i
$738$		0			0
$739$	−44.4674			−1.63576			−0.817879	−	0.575390i	$-0.804850\pi$
$739$	−44.4674			−1.63576			−0.817879	+	0.575390i	$0.804850\pi$
$740$		0			0
$741$	−29.4891			−1.08331
$742$		0			0
$743$	17.7446	−	30.7345i	0.650985	−	1.12754i	−0.331899	−	0.943315i	$-0.607689\pi$
$743$	17.7446	−	30.7345i	0.650985	−	1.12754i	0.982884	−	0.184224i	$-0.0589772\pi$
$744$		0			0
$745$	−12.4307	+	21.5306i	−0.455426	+	0.788821i
$746$		0			0
$747$	4.00000	−	6.92820i	0.146352	−	0.253490i
$748$		0			0
$749$	14.7446	+	25.5383i	0.538755	+	0.933150i
$750$		0			0
$751$	−33.1168			−1.20845			−0.604225	−	0.796813i	$-0.706517\pi$
$751$	−33.1168			−1.20845			−0.604225	+	0.796813i	$0.706517\pi$
$752$		0			0
$753$	−0.627719	+	1.08724i	−0.0228753	+	0.0396213i
$754$		0			0
$755$	−22.9783	−	39.7995i	−0.836264	−	1.44845i
$756$		0			0
$757$	15.8723	+	27.4916i	0.576888	+	0.999199i	0.995834	+	0.0911879i	$0.0290664\pi$
$757$	15.8723	+	27.4916i	0.576888	+	0.999199i	−0.418946	+	0.908011i	$0.637600\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	2.43070	+	4.21010i	0.0881129	+	0.152616i	0.906713	−	0.421747i	$-0.138583\pi$
$761$	2.43070	+	4.21010i	0.0881129	+	0.152616i	−0.818601	+	0.574363i	$0.805250\pi$
$762$		0			0
$763$	68.8397			2.49216
$764$		0			0
$765$	12.4307	+	21.5306i	0.449433	+	0.778441i
$766$		0			0
$767$	−17.4891			−0.631496
$768$		0			0
$769$	21.1168			0.761493			0.380746	−	0.924679i	$-0.375667\pi$
$769$	21.1168			0.761493			0.380746	+	0.924679i	$0.375667\pi$
$770$		0			0
$771$	−8.86141			−0.319136
$772$		0			0
$773$	−16.4307	+	28.4588i	−0.590971	+	1.02359i	0.403131	+	0.915142i	$0.367922\pi$
$773$	−16.4307	+	28.4588i	−0.590971	+	1.02359i	−0.994102	+	0.108450i	$0.965411\pi$
$774$		0			0
$775$	−11.5584	−	20.0198i	−0.415191	−	0.719132i
$776$		0			0
$777$	11.1861	+	24.1287i	0.401301	+	0.865612i
$778$		0			0
$779$	−4.62772	−	8.01544i	−0.165805	−	0.287183i
$780$		0			0
$781$	11.4891	−	19.8997i	0.411113	−	0.712069i
$782$		0			0
$783$	−1.37228			−0.0490413
$784$		0			0
$785$	−55.6060			−1.98466
$786$		0			0
$787$	−11.1168			−0.396273			−0.198136	−	0.980174i	$-0.563489\pi$
$787$	−11.1168			−0.396273			−0.198136	+	0.980174i	$0.563489\pi$
$788$		0			0
$789$	−7.62772	−	13.2116i	−0.271554	−	0.470345i
$790$		0			0
$791$	−32.7446			−1.16426
$792$		0			0
$793$	17.7446	+	30.7345i	0.630128	+	1.09141i
$794$		0			0
$795$	19.3723	−	33.5538i	0.687064	−	1.19003i
$796$		0			0
$797$	−19.6060	−	33.9585i	−0.694479	−	1.20287i	−0.970356	−	0.241680i	$-0.922302\pi$
$797$	−19.6060	−	33.9585i	−0.694479	−	1.20287i	0.275877	−	0.961193i	$-0.411032\pi$
$798$		0			0
$799$	−7.37228	−	12.7692i	−0.260813	−	0.451741i
$800$		0			0
$801$	−4.68614	+	8.11663i	−0.165577	+	0.286787i
$802$		0			0
$803$	−16.7446			−0.590903
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.00000	+	1.73205i	−0.0352017	+	0.0609711i
$808$		0			0
$809$	3.51087	−	6.08101i	0.123436	−	0.213797i	−0.797685	−	0.603075i	$-0.793942\pi$
$809$	3.51087	−	6.08101i	0.123436	−	0.213797i	0.921120	+	0.389278i	$0.127275\pi$
$810$		0			0
$811$	−17.4891	+	30.2921i	−0.614126	+	1.06370i	0.376411	+	0.926453i	$0.377158\pi$
$811$	−17.4891	+	30.2921i	−0.614126	+	1.06370i	−0.990537	+	0.137245i	$0.956175\pi$
$812$		0			0
$813$	9.86141			0.345855
$814$		0			0
$815$	−44.7011			−1.56581
$816$		0			0
$817$	−12.2337	+	21.1894i	−0.428003	+	0.741322i
$818$		0			0
$819$	−9.55842	+	16.5557i	−0.333998	+	0.578502i
$820$		0			0
$821$	11.0000	−	19.0526i	0.383903	−	0.664939i	−0.607714	−	0.794156i	$-0.707913\pi$
$821$	11.0000	−	19.0526i	0.383903	−	0.664939i	0.991616	+	0.129217i	$0.0412465\pi$
$822$		0			0
$823$	13.4198	+	23.2438i	0.467786	+	0.810229i	0.999322	−	0.0368065i	$-0.0117185\pi$
$823$	13.4198	+	23.2438i	0.467786	+	0.810229i	−0.531537	+	0.847035i	$0.678385\pi$
$824$		0			0
$825$	−12.7446			−0.443709
$826$		0			0
$827$	16.0000	−	27.7128i	0.556375	−	0.963669i	−0.441421	−	0.897300i	$-0.645525\pi$
$827$	16.0000	−	27.7128i	0.556375	−	0.963669i	0.997795	−	0.0663686i	$-0.0211413\pi$
$828$		0			0
$829$	−5.06930	−	8.78028i	−0.176064	−	0.304952i	0.764465	−	0.644665i	$-0.223003\pi$
$829$	−5.06930	−	8.78028i	−0.176064	−	0.304952i	−0.940529	+	0.339714i	$0.889670\pi$
$830$		0			0
$831$	15.4307	+	26.7268i	0.535285	+	0.927141i
$832$		0			0
$833$	44.6644	−	77.3610i	1.54753	−	2.68040i
$834$		0			0
$835$	36.2337	+	62.7586i	1.25392	+	2.17185i
$836$		0			0
$837$	3.62772			0.125392
$838$		0			0
$839$	2.00000	+	3.46410i	0.0690477	+	0.119594i	0.898482	−	0.439010i	$-0.144671\pi$
$839$	2.00000	+	3.46410i	0.0690477	+	0.119594i	−0.829435	+	0.558604i	$0.811337\pi$
$840$		0			0
$841$	−27.1168			−0.935064
$842$		0			0
$843$	10.1168			0.348443
$844$		0			0
$845$	20.6277			0.709615
$846$		0			0
$847$	−15.3030	+	26.5055i	−0.525817	+	0.910741i
$848$		0			0
$849$	8.55842	+	14.8236i	0.293724	+	0.508745i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−2.80298	−	4.85491i	−0.0959724	−	0.166229i	0.814042	−	0.580807i	$-0.197263\pi$
$853$	−2.80298	−	4.85491i	−0.0959724	−	0.166229i	−0.910014	+	0.414577i	$0.863929\pi$
$854$		0			0
$855$	−11.3723	+	19.6974i	−0.388924	+	0.673636i
$856$		0			0
$857$	−43.8397			−1.49753			−0.748767	−	0.662833i	$-0.769354\pi$
$857$	−43.8397			−1.49753			−0.748767	+	0.662833i	$0.769354\pi$
$858$		0			0
$859$	2.60597			0.0889145			0.0444573	−	0.999011i	$-0.485844\pi$
$859$	2.60597			0.0889145			0.0444573	+	0.999011i	$0.485844\pi$
$860$		0			0
$861$	−6.00000			−0.204479
$862$		0			0
$863$	−7.62772	−	13.2116i	−0.259651	−	0.449728i	0.706498	−	0.707715i	$-0.250274\pi$
$863$	−7.62772	−	13.2116i	−0.259651	−	0.449728i	−0.966148	+	0.257987i	$0.916941\pi$
$864$		0			0
$865$	19.8397			0.674569
$866$		0			0
$867$	−18.6753	−	32.3465i	−0.634245	−	1.09855i
$868$		0			0
$869$	4.37228	−	7.57301i	0.148319	−	0.256897i
$870$		0			0
$871$	28.6753	+	49.6670i	0.971624	+	1.68290i
$872$		0			0
$873$	2.87228	+	4.97494i	0.0972120	+	0.168376i
$874$		0			0
$875$	10.1168	−	17.5229i	0.342012	−	0.592382i
$876$		0			0
$877$	−47.0000			−1.58708			−0.793539	−	0.608520i	$-0.791764\pi$
$877$	−47.0000			−1.58708			−0.793539	+	0.608520i	$0.791764\pi$
$878$		0			0
$879$	7.94158	+	13.7552i	0.267863	+	0.463952i
$880$		0			0
$881$	−5.05842	+	8.76144i	−0.170423	+	0.295181i	−0.938568	−	0.345095i	$-0.887847\pi$
$881$	−5.05842	+	8.76144i	−0.170423	+	0.295181i	0.768145	+	0.640276i	$0.221180\pi$
$882$		0			0
$883$	19.4891	−	33.7562i	0.655861	−	1.13599i	−0.325816	−	0.945433i	$-0.605639\pi$
$883$	19.4891	−	33.7562i	0.655861	−	1.13599i	0.981677	−	0.190552i	$-0.0610277\pi$
$884$		0			0
$885$	−6.74456	+	11.6819i	−0.226716	+	0.392684i
$886$		0			0
$887$	20.0000			0.671534			0.335767	−	0.941945i	$-0.391004\pi$
$887$	20.0000			0.671534			0.335767	+	0.941945i	$0.391004\pi$
$888$		0			0
$889$	62.8397			2.10757
$890$		0			0
$891$	1.00000	−	1.73205i	0.0335013	−	0.0580259i
$892$		0			0
$893$	6.74456	−	11.6819i	0.225698	−	0.390921i
$894$		0			0
$895$	−20.2337	+	35.0458i	−0.676338	+	1.17145i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−4.97825			−0.166034
$900$		0			0
$901$	−42.3505	+	73.3533i	−1.41090	+	2.44375i
$902$		0			0
$903$	7.93070	+	13.7364i	0.263917	+	0.457118i
$904$		0			0
$905$	26.5475	+	45.9817i	0.882470	+	1.52848i
$906$		0			0
$907$	−15.6753	+	27.1504i	−0.520489	+	0.901513i	0.479228	+	0.877691i	$0.340917\pi$
$907$	−15.6753	+	27.1504i	−0.520489	+	0.901513i	−0.999716	+	0.0238221i	$0.992416\pi$
$908$		0			0
$909$	7.43070	+	12.8704i	0.246461	+	0.426883i
$910$		0			0
$911$	35.7228			1.18355			0.591775	−	0.806103i	$-0.298427\pi$
$911$	35.7228			1.18355			0.591775	+	0.806103i	$0.298427\pi$
$912$		0			0
$913$	−8.00000	−	13.8564i	−0.264761	−	0.458580i
$914$		0			0
$915$	27.3723			0.904900
$916$		0			0
$917$	−3.25544			−0.107504
$918$		0			0
$919$	−16.6060			−0.547780			−0.273890	−	0.961761i	$-0.588310\pi$
$919$	−16.6060			−0.547780			−0.273890	+	0.961761i	$0.588310\pi$
$920$		0			0
$921$	4.55842	−	7.89542i	0.150205	−	0.260163i
$922$		0			0
$923$	25.1168	+	43.5036i	0.826731	+	1.43194i
$924$		0			0
$925$	−16.3030	−	35.1658i	−0.536039	−	1.15624i
$926$		0			0
$927$	0.627719	+	1.08724i	0.0206170	+	0.0357097i
$928$		0			0
$929$	24.8030	−	42.9600i	0.813760	−	1.40947i	−0.0964557	−	0.995337i	$-0.530751\pi$
$929$	24.8030	−	42.9600i	0.813760	−	1.40947i	0.910215	−	0.414136i	$-0.135916\pi$
$930$		0			0
$931$	81.7228			2.67836
$932$		0			0
$933$	−16.9783			−0.555843
$934$		0			0
$935$	49.7228			1.62611
$936$		0			0
$937$	1.01087	+	1.75089i	0.0330238	+	0.0571990i	0.882065	−	0.471128i	$-0.156153\pi$
$937$	1.01087	+	1.75089i	0.0330238	+	0.0571990i	−0.849041	+	0.528327i	$0.822820\pi$
$938$		0			0
$939$	−17.0000			−0.554774
$940$		0			0
$941$	−20.6644	−	35.7918i	−0.673640	−	1.16678i	−0.976864	−	0.213859i	$-0.931397\pi$
$941$	−20.6644	−	35.7918i	−0.673640	−	1.16678i	0.303225	−	0.952919i	$-0.401937\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	7.37228	+	12.7692i	0.239820	+	0.415381i
$946$		0			0
$947$	−18.6060	−	32.2265i	−0.604613	−	1.04722i	−0.992113	−	0.125350i	$-0.959995\pi$
$947$	−18.6060	−	32.2265i	−0.604613	−	1.04722i	0.387500	−	0.921870i	$-0.373339\pi$
$948$		0			0
$949$	18.3030	−	31.7017i	0.594140	−	1.02908i
$950$		0			0
$951$	−30.1168			−0.976606
$952$		0			0
$953$	−2.86141	−	4.95610i	−0.0926901	−	0.160544i	0.815952	−	0.578119i	$-0.196213\pi$
$953$	−2.86141	−	4.95610i	−0.0926901	−	0.160544i	−0.908642	+	0.417576i	$0.862880\pi$
$954$		0			0
$955$	−18.9783	+	32.8713i	−0.614122	+	1.06369i
$956$		0			0
$957$	−1.37228	+	2.37686i	−0.0443596	+	0.0768330i
$958$		0			0
$959$	10.1168	−	17.5229i	0.326690	−	0.565844i
$960$		0			0
$961$	−17.8397			−0.575473
$962$		0			0
$963$	6.74456			0.217340
$964$		0			0
$965$	−7.56930	+	13.1104i	−0.243664	+	0.422039i
$966$		0			0
$967$	16.3030	−	28.2376i	0.524269	−	0.908060i	−0.475332	−	0.879806i	$-0.657672\pi$
$967$	16.3030	−	28.2376i	0.524269	−	0.908060i	0.999601	−	0.0282535i	$-0.00899456\pi$
$968$		0			0
$969$	24.8614	−	43.0612i	0.798663	−	1.38333i
$970$		0			0
$971$	−22.9783	−	39.7995i	−0.737407	−	1.27723i	−0.953659	−	0.300889i	$-0.902717\pi$
$971$	−22.9783	−	39.7995i	−0.737407	−	1.27723i	0.216252	−	0.976338i	$-0.430617\pi$
$972$		0			0
$973$	−62.8397			−2.01455
$974$		0			0
$975$	13.9307	−	24.1287i	0.446140	−	0.772736i
$976$		0			0
$977$	7.37228	+	12.7692i	0.235860	+	0.408522i	0.959522	−	0.281633i	$-0.0908759\pi$
$977$	7.37228	+	12.7692i	0.235860	+	0.408522i	−0.723662	+	0.690154i	$0.757543\pi$
$978$		0			0
$979$	9.37228	+	16.2333i	0.299539	+	0.518817i
$980$		0			0
$981$	7.87228	−	13.6352i	0.251343	−	0.435338i
$982$		0			0
$983$	−4.62772	−	8.01544i	−0.147601	−	0.255653i	0.782739	−	0.622350i	$-0.213822\pi$
$983$	−4.62772	−	8.01544i	−0.147601	−	0.255653i	−0.930340	+	0.366697i	$0.880489\pi$
$984$		0			0
$985$	65.3288			2.08155
$986$		0			0
$987$	−4.37228	−	7.57301i	−0.139171	−	0.241052i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	52.2337			1.65926			0.829629	−	0.558315i	$-0.188552\pi$
$991$	52.2337			1.65926			0.829629	+	0.558315i	$0.188552\pi$
$992$		0			0
$993$	−4.60597			−0.146166
$994$		0			0
$995$	−20.8614	+	36.1330i	−0.661351	+	1.14549i
$996$		0			0
$997$	3.51087	+	6.08101i	0.111191	+	0.192588i	0.916251	−	0.400606i	$-0.131200\pi$
$997$	3.51087	+	6.08101i	0.111191	+	0.192588i	−0.805060	+	0.593193i	$0.797867\pi$
$998$		0			0
$999$	6.05842	+	0.543620i	0.191680	+	0.0171994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1776.2.q.h.433.1		4
4.3	odd	2		222.2.e.c.211.1	yes	4
12.11	even	2		666.2.f.g.433.2		4
37.10	even	3	inner	1776.2.q.h.1009.1		4
148.11	odd	6		8214.2.a.o.1.1		2
148.47	odd	6		222.2.e.c.121.1	✓	4
148.63	odd	6		8214.2.a.m.1.2		2
444.47	even	6		666.2.f.g.343.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
222.2.e.c.121.1	✓	4	148.47	odd	6
222.2.e.c.211.1	yes	4	4.3	odd	2
666.2.f.g.343.2		4	444.47	even	6
666.2.f.g.433.2		4	12.11	even	2
1776.2.q.h.433.1		4	1.1	even	1	trivial
1776.2.q.h.1009.1		4	37.10	even	3	inner
8214.2.a.m.1.2		2	148.63	odd	6
8214.2.a.o.1.1		2	148.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1776 = 2^{4} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1776.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-1.68614 + 2.92048i) q^{5} +(2.18614 - 3.78651i) q^{7} +(-0.500000 - 0.866025i) q^{9} -2.00000 q^{11} +(2.18614 - 3.78651i) q^{13} +(-1.68614 - 2.92048i) q^{15} +(3.68614 + 6.38458i) q^{17} +(-3.37228 + 5.84096i) q^{19} +(2.18614 + 3.78651i) q^{21} +(-3.18614 - 5.51856i) q^{25} +1.00000 q^{27} -1.37228 q^{29} +3.62772 q^{31} +(1.00000 - 1.73205i) q^{33} +(7.37228 + 12.7692i) q^{35} +(6.05842 + 0.543620i) q^{37} +(2.18614 + 3.78651i) q^{39} +(-0.686141 + 1.18843i) q^{41} +3.62772 q^{43} +3.37228 q^{45} -2.00000 q^{47} +(-6.05842 - 10.4935i) q^{49} -7.37228 q^{51} +(5.74456 + 9.94987i) q^{53} +(3.37228 - 5.84096i) q^{55} +(-3.37228 - 5.84096i) q^{57} +(-2.00000 - 3.46410i) q^{59} +(-4.05842 + 7.02939i) q^{61} -4.37228 q^{63} +(7.37228 + 12.7692i) q^{65} +(-6.55842 + 11.3595i) q^{67} +(-5.74456 + 9.94987i) q^{71} +8.37228 q^{73} +6.37228 q^{75} +(-4.37228 + 7.57301i) q^{77} +(-2.18614 + 3.78651i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(4.00000 + 6.92820i) q^{83} -24.8614 q^{85} +(0.686141 - 1.18843i) q^{87} +(-4.68614 - 8.11663i) q^{89} +(-9.55842 - 16.5557i) q^{91} +(-1.81386 + 3.14170i) q^{93} +(-11.3723 - 19.6974i) q^{95} -5.74456 q^{97} +(1.00000 + 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - q^{5} + 3 q^{7} - 2 q^{9} - 8 q^{11} + 3 q^{13} - q^{15} + 9 q^{17} - 2 q^{19} + 3 q^{21} - 7 q^{25} + 4 q^{27} + 6 q^{29} + 26 q^{31} + 4 q^{33} + 18 q^{35} + 7 q^{37} + 3 q^{39} + 3 q^{41}+ \cdots + 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - q^5 + 3 * q^7 - 2 * q^9 - 8 * q^11 + 3 * q^13 - q^15 + 9 * q^17 - 2 * q^19 + 3 * q^21 - 7 * q^25 + 4 * q^27 + 6 * q^29 + 26 * q^31 + 4 * q^33 + 18 * q^35 + 7 * q^37 + 3 * q^39 + 3 * q^41 + 26 * q^43 + 2 * q^45 - 8 * q^47 - 7 * q^49 - 18 * q^51 + 2 * q^55 - 2 * q^57 - 8 * q^59 + q^61 - 6 * q^63 + 18 * q^65 - 9 * q^67 + 22 * q^73 + 14 * q^75 - 6 * q^77 - 3 * q^79 - 2 * q^81 + 16 * q^83 - 42 * q^85 - 3 * q^87 - 13 * q^89 - 21 * q^91 - 13 * q^93 - 34 * q^95 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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